The curve that will be investigated is made up from the vertices of the
angles which have size , share the common chord
AB and lie
in one and the same halfplane with respect to the line through
AB.
It is a well-known fact that in Euclidean geometry these points form an
arc of a circle. Also, it is clear that any one of the given angles
can be moved into any other by a rotation. In non-Euclidean geometry
all this does not hold. A sketch of a convexity proof for this latter
setting will be provided.